The present invention relates to golf balls having improved aerodynamic characteristics that yield improved flight performance and longer ball flight. The improved aerodynamic characteristics are obtained through the use of specific dimple arrangements and dimple profiles. The aerodynamic improvements are applicable to golf balls of any size and weight. The invention further relates to golf balls with symmetric flight characteristics.
The flight of a golf ball is determined by many factors, however, the majority of the properties that determine flight are outside of the control of a golfer. While a golfer can control the speed, the launch angle, and the spin rate of a golf ball by hitting the ball with a particular club, the final resting point of the ball depends upon golf ball construction and materials, as well as environmental conditions, e.g., terrain and weather. Since flight distance and consistency are critical factor in reducing golf scores, manufacturers continually strive to make even the slightest incremental improvements in golf ball flight consistency and flight distance, e.g., one or more yards, through various aerodynamic properties and golf ball constructions. Flight consistency is a significant problem for manufacturers because the many of golf ball dimple patterns and/or dimple shapes that yield increased flight distance also result in asymmetric flight performance. Asymmetric flight performance prescribes that the overall flight distance is a function of ball orientation when struck with a club.
Historically, manufacturers improved flight performance via iterative testing, where golf balls with numerous dimple patterns and dimple profiles are produced and tested using mechanical golfers. Flight performance is characterized in these tests by measuring the landing position of the various ball designs. To determine if a particular ball design has desirable flight characteristics for a broad range of players, i.e., high and low swing speed players, manufacturers perform the mechanical golfer test with different ball launch conditions, which involves immense time and financial commitments. Furthermore, it is difficult to identify incremental performance improvements using these methods due to the statistical noise generated by environmental conditions, which necessitates large sample sizes for sufficient confidence intervals.
Another more precise method of determining specific dimple arrangements and dimple shapes that results in an aerodynamic advantage involves the direct measurement of aerodynamic characteristics as opposed to ball landing positions. These aerodynamic characteristics define the forces acting upon the golf ball throughout flight.
Aerodynamic forces acting on a golf ball are typically resolved into orthogonal components of lift and drag. Lift is defined as the aerodynamic force component acting perpendicular to the flight path. It results from a difference in pressure that is created by a distortion in the air flow that results from the back spin of the ball. A boundary layer forms at the stagnation point of the ball, B, then grows and separates at points S1 and S2, as shown in FIG. 1. Due to the ball backspin, the top of the ball moves in the direction of the airflow, which retards the separation of the boundary layer. In contrast, the bottom of the ball moves against the direction of airflow, thus advancing the separation of the boundary layer at the bottom of the ball. Therefore, the position of separation of the boundary layer at the top of the ball, S1, is further back than the position of separation of the boundary layer at the bottom of the ball, S2. This asymmetrical separation creates an arch in the flow pattern, requiring the air over the top of the ball to move faster and, thus, have lower pressure than the air underneath the ball.
Drag is defined as the aerodynamic force component acting parallel to the ball flight direction. As the ball travels through the air, the air surrounding the ball has different velocities and, accordingly, different pressures. The air exerts maximum pressure at the stagnation point, B, on the front of the ball, as shown in FIG. 1. The air then flows over the sides of the ball and has increased velocity and reduced pressure. The air separates from the surface of the ball at points S1 and S2, leaving a large turbulent flow area with low pressure, i.e., the wake. The difference between the high pressure in front of the ball and the low pressure behind the ball reduces the ball speed and acts as the primary source of drag for a golf ball.
The dimples on a golf ball are used to adjust drag and lift properties of a golf ball and, therefore, the majority of golf ball manufacturers research dimple patterns, shape, volume, and cross-section in order to improve overall flight distance of a golf ball. The dimples create a thin turbulent boundary layer around the ball. The turbulence energizes the boundary layer and aids in maintaining attachment to and around the ball to reduce the area of the wake. The pressure behind the ball is increased and the drag is substantially reduced.
There is minimal prior art disclosing preferred aerodynamic characteristics for golf balls. U.S. Pat. No. 5,935,023 discloses preferred lift and drag coefficients for a single speed with a functional dependence on spin ratio. U.S. Pat. Nos. 6,213,898 and 6,290,615 disclose golf ball dimple patterns that reduce high-speed drag and increase low speed lift. It has now been discovered, contrary to the disclosures of these patents, that reduced high-speed drag and increased low speed lift does not necessarily result in improved flight performance. For example, excessive high-speed lift or excessive low-speed drag may result in undesirable flight performance characteristics. The prior art is silent, however, as to aerodynamic features that influence other portions of golf ball flight, such as flight consistency, as well as enhanced aerodynamic coefficients for balls of varying size and weight.
Thus, there is a need to optimize the aerodynamics of a golf ball to improve flight distance and consistency. There is also a need to develop dimple arrangements and profiles that result in longer distance and more consistent flights regardless of the swing-speed of a player, the orientation of the ball when impacted, or the physical properties of the ball being played.
The present invention is directed to a golf ball with improved aerodynamic performance. In one embodiment, a golf ball with a plurality of dimples has an aerodynamic coefficient magnitude defined by Cmag=(CL2+CD2) and an aerodynamic force angle defined by Angle=tanxe2x88x921(CL/CD), wherein CL is a lift coefficient and CD is a drag coefficient, wherein the golf ball has a first aerodynamic coefficient magnitude from about 0.24 to about 0.27 and a first aerodynamic force angle of about 31 degrees to about 35 degrees at a Reynolds Number of about 230000 and a spin ratio of about 0.085 and a second aerodynamic coefficient magnitude from about 0.25 to about 0.28 and a second aerodynamic force angle of about 34 degrees to about 38 degrees at a Reynolds Number of about 207000 and a spin ratio of about 0.095.
In another embodiment, the golf ball has a third aerodynamic coefficient magnitude from about 0.26 to about 0.29 and a third aerodynamic force angle from about 35 degrees to about 39 degrees at a Reynolds Number of about 184000 and a spin ratio of about 0.106 and a fourth aerodynamic coefficient magnitude from about 0.27 to about 0.30 and a fourth aerodynamic force angle of about 37 degrees to about 42 degrees at a Reynolds Number of about 161000 and a spin ratio of about 0.122. In yet another embodiment, a fifth aerodynamic coefficient magnitude is from about 0.29 to about 0.32 and a fifth aerodynamic force angle is from about 39 degrees to about 43 degrees at a Reynolds Number of about 138000 and a spin ratio of about 0.142 and a sixth aerodynamic coefficient magnitude is from about 0.32 to about 0.35 and a sixth aerodynamic force angle is from about 40 degrees to about 44 degrees at a Reynolds Number of about 115000 and a spin ratio of about 0.170. In a further embodiment, the golf ball has a seventh aerodynamic coefficient magnitude from about 0.36 to about 0.40 and a seventh aerodynamic force angle of about 41 degrees to about 45 degrees at a Reynolds Number of about 92000 and a spin ratio of about 0.213 and an eighth aerodynamic coefficient magnitude from about 0.40 to about 0.45 and an eighth aerodynamic force angle of about 40 degrees to about 44 degrees at a Reynolds Number of about 69000 and a spin ratio of about 0.284.
The aerodynamic coefficient magnitudes may vary from each other by about 6 percent or less, and more preferably, about 3 percent or less, at any two axes of ball rotation. In another embodiment, the plurality of dimples cover about 80 percent or greater of the ball surface. In yet another embodiment, at least 80 percent of the dimples have a diameter greater than about 6.5 percent of the ball diameter. The dimples are preferably arranged in an icosahedron or an octahedron pattern. In one embodiment, the dimples have at least three different dimple diameters. In another embodiment, at least 10 percent of the plurality of dimples have a shape defined by catenary curve. In yet another embodiment, at least a first portion of the dimples have a shape factor of less than 60 and a second portion of the dimples have a shape factor of greater than 60. The golf ball may have at least one core and at least one cover layer, wherein at least one of the layers comprises urethane, ionomer, balata, polyurethane, and mixtures thereof.
The present invention is also directed to a golf ball with a plurality of dimples having an aerodynamic coefficient magnitude defined by Cmag=(CL2+CD2) and an aerodynamic force angle defined by Angle=tanxe2x88x921(CL/CD), wherein CL is a lift coefficient and CD is a drag coefficient, wherein the golf ball comprises a first aerodynamic coefficient magnitude from about 0.40 to about 0.45 and a first aerodynamic force angle of about 40 degrees to about 44 degrees at a Reynolds Number of about 69000 and a spin ratio of about 0.284 and a second aerodynamic coefficient magnitude from about 0.36 to about 0.40 and a second aerodynamic force angle of about 41 degrees to about 45 degrees at a Reynolds Number of about 92000 and a spin ratio of about 0.213.
The golf ball may also have a third aerodynamic coefficient magnitude from about 0.32 to about 0.35 and a third aerodynamic force angle of about 40 degrees to about 44 degrees at a Reynolds Number of about 115000 and a spin ratio of about 0.170 and a fourth aerodynamic coefficient magnitude from about 0.29 to about 0.32 and a fourth aerodynamic force angle of about 39 degrees to about 43 degrees at a Reynolds Number of about 138000 and a spin ratio of about 0.142. In another embodiment, the golf ball has a fifth aerodynamic coefficient magnitude from about 0.27 to about 0.30 and a fifth aerodynamic force angle of about 37 degrees to about 42 degrees at a Reynolds Number of about 161000 and a spin ratio of about 0.122 and a sixth aerodynamic coefficient magnitude from about 0.26 to about 0.29 and a sixth aerodynamic force angle of about 35 degrees to about 39 degrees at a Reynolds Number of about 184000 and a spin ratio of about 0.106.
In one embodiment, the aerodynamic coefficient magnitudes vary from each other by about 6 percent, and more preferably, about 3 percent, or less at any two axes of ball rotation. In another embodiment, the plurality of dimples cover about 80 percent or greater of the ball surface. In yet another embodiment, at least 80 percent of the dimples have a diameter greater than about 6.5 percent of the ball diameter and the dimples are preferably arranged in an icosahedron or an octahedron pattern. In one embodiment, the dimples have at least three different dimple diameters. In another embodiment, at least 10 percent of the plurality of dimples have a shape defined by catenary curve. In yet another embodiment, at least a first portion of the dimples have a shape factor of less than 60 and a second portion of the dimples have a shape factor of greater than 60. The golf ball may have at least one core and at least one cover layer, wherein at least one of the layers comprises urethane, ionomer, balata, polyurethane, and mixtures thereof.
The present invention is also related to a golf ball with a plurality of dimples having an aerodynamic coefficient magnitude defined by Cmag=(CL2+CD2) and an aerodynamic force angle defined by Angle=tanxe2x88x921(CL/CD), wherein CL is a lift coefficient and CD is a drag coefficient, wherein the golf ball has a first aerodynamic coefficient magnitude from about 0.40 to about 0.45 and a first aerodynamic force angle of about 40 degrees to about 44 degrees at a Reynolds Number of about 69000 and a spin ratio of about 0.284 for a ball weight W of 1.62 ounces and a diameter D of 1.68 inches and a second aerodynamic coefficient magnitude from about 0.36 to about 0.40 and a second aerodynamic force angle of about 41 degrees to about 45 degrees at a Reynolds Number of about 92000 and a spin ratio of about 0.213 for a ball weight of 1.62 ounces and a diameter of 1.68 inches, wherein the aerodynamic coefficient magnitudes and force angles are adjusted for ball weight and diameter in the following manner:
Adjusted Cmag=Cmag((sin(Angle)*(W/1.62)*(1.68/D)2)2+(cos(Angle))2)
Adjusted Angle=tanxe2x88x921(tan(Angle)*(W/1.62)*(1.68/D)2).
The golf ball may also have a third aerodynamic coefficient magnitude from about 0.32 to about 0.35 and a third aerodynamic force angle of about 40 degrees to about 44 degrees at a Reynolds Number of about 115000 and a spin ratio of about 0.170 and a fourth aerodynamic coefficient magnitude from about 0.29 to about 0.32 and a fourth aerodynamic force angle of about 39 degrees to about 43 degrees at a Reynolds Number of about 138000 and a spin ratio of about 0.142. In another embodiment, the golf ball has a fifth aerodynamic coefficient magnitude from about 0.27 to about 0.30 and a fifth aerodynamic force angle of about 37 degrees to about 42 degrees at a Reynolds Number of about 161000 and a spin ratio of about 0.122 and a sixth aerodynamic coefficient magnitude from about 0.26 to about 0.29 and a sixth aerodynamic force angle of about 35 degrees to about 39 degrees at a Reynolds Number of about 184000 and a spin ratio of about 0.106. In yet another embodiment, a seventh aerodynamic coefficient magnitude is from about 0.25 to about 0.28 and a seventh aerodynamic force angle is from about 34 degrees to about 38 degrees at a Reynolds Number of about 207000 and a spin ratio of about 0.095 and an eighth aerodynamic coefficient magnitude is from about 0.24 to about 0.27 and an eighth aerodynamic force angle is from about 31 degrees to about 35 degrees at a Reynolds Number of about 230000 and a spin ratio of about 0.085.
In one embodiment, the aerodynamic coefficient magnitudes vary from each other by about 6 percent, and more preferably, about 3 percent, or less at any two axes of ball rotation. In another embodiment, the plurality of dimples cover about 80 percent or greater of the ball surface. In yet another embodiment, at least 80 percent of the dimples have a diameter greater than about 6.5 percent of the ball diameter and the dimples are preferably arranged in an icosahedron or an octahedron pattern. In one embodiment, the dimples have at least three different dimple diameters. In another embodiment, at least 10 percent of the plurality of dimples have a shape defined by catenary curve. In yet another embodiment, at least a first portion of the dimples have a shape factor of less than 60 and a second portion of the dimples have a shape factor of greater than 60. The golf ball may have at least one core and at least one cover layer, wherein at least one of the layers comprises urethane, ionomer, balata, polyurethane, and mixtures thereof.
The present invention is further directed to a golf ball with a plurality of dimples having an aerodynamic coefficient magnitude defined by Cmag=(CL2+CD2) and an aerodynamic force angle defined by Angle=tanxe2x88x921(CL/CD), wherein CL is a lift coefficient and CD is a drag coefficient, wherein the golf ball has a first aerodynamic coefficient magnitude from about 0.40 to about 0.44 and a first aerodynamic force angle of about 40 degrees to about 42 degrees at a Reynolds Number of about 69000 and a spin ratio of about 0.284 and a second aerodynamic coefficient magnitude from about 0.36 to about 0.39 and a second aerodynamic force angle of about 41 degrees to about 43 degrees at a Reynolds Number of about 92000 and a spin ratio of about 0.213.
In one embodiment, the golf ball further includes a third aerodynamic coefficient magnitude from about 0.32 to about 0.344 and a third aerodynamic force angle of about 40 degrees to about 42 degrees at a Reynolds Number of about 115000 and a spin ratio of about 0.170 and a fourth aerodynamic coefficient magnitude from about 0.29 to about 0.311 and a fourth aerodynamic force angle of about 39 degrees to about 41 degrees at a Reynolds Number of about 138000 and a spin ratio of about 0.142. The golf ball may also include a fifth aerodynamic coefficient magnitude from about 0.27 to about 0.291 and a fifth aerodynamic force angle of about 37 degrees to about 40 degrees at a Reynolds Number of about 161000 and a spin ratio of about 0.122 and a sixth aerodynamic coefficient magnitude from about 0.26 to about 0.28 and a sixth aerodynamic force angle of about 35 degrees to about 38 degrees at a Reynolds Number of about 184000 and a spin ratio of about 0.106. In another embodiment, a seventh aerodynamic coefficient magnitude from about 0.25 to about 0.271 and a seventh aerodynamic force angle of about 34 degrees to about 36 degrees at a Reynolds Number of about 207000 and a spin ratio of about 0.095 and an eighth aerodynamic coefficient magnitude from about 0.24 to about 0.265 and an eighth aerodynamic force angle of about 31 degrees to about 33 degrees at a Reynolds Number of about 230000 and a spin ratio of about 0.085 may further define the golf ball.
In one embodiment, the aerodynamic coefficient magnitudes vary from each other by about 6 percent, and more preferably, about 3 percent, or less at any two axes of ball rotation. In another embodiment, the plurality of dimples cover about 80 percent or greater of the ball surface. In yet another embodiment, at least 80 percent of the dimples have a diameter greater than about 6.5 percent of the ball diameter and the dimples are preferably arranged in an icosahedron or an octahedron pattern. In one embodiment, the dimples have at least three different dimple diameters. In another embodiment, at least 10 percent of the plurality of dimples have a shape defined by catenary curve. In yet another embodiment, at least a first portion of the dimples have a shape factor of less than 60 and a second portion of the dimples have a shape factor of greater than 60. The golf ball may have at least one core and at least one cover layer, wherein at least one of the layers comprises urethane, ionomer, balata, polyurethane, and mixtures thereof.
The present invention is also directed to a golf ball dimple pattern that provides a surprisingly better dimple packing than any previous pattern so that a greater percentage of the surface of the golf ball is covered by dimples. The prior art golf balls have dimple patterns that leave many large spaces between adjacent dimples and/or use small dimples to fill in the spaces. The golf balls according to the present invention have triangular regions with a plurality of dimple sizes arranged to provide a remarkably high percentage of dimple coverage while avoiding groupings of relatively large dimples.
The triangular regions have a first set of dimples formed in a large triangle and a second set of dimples formed in a small triangle inside of and adjacent to the large triangle. The first set of dimples forming the large triangle comprises dimples that increase in size from the dimples on the points of the triangle toward the midpoint of the triangle side. Thus, the dimples close to or on the midpoint of the sides of the triangle are the largest dimples on the large triangle. Each dimple diameter along the triangle side is equal to or greater than the adjacent dimple toward the vertex or triangle point. Through this layout and with proper sizing, as set forth below, the dimple coverage is greater than 80 percent of the surface of the golf ball.
Further, the dimples are arranged so that there are three or less great circle paths that do not intersect any dimples to minimize undimpled surface area. Great circles take up a significant amount of the surface area and an intersection of more than two great circles creates very small angles that have to be filled with very small dimples or large gaps are created.
Still further, the dimples are arranged such that there are no more than two adjacent dimples of the largest diameter. Thus, the largest dimples are more evenly spaced over the ball and are not clumped together.
In one embodiment of the present invention, dimples cover more than 80 percent of the outer surface. More importantly, the dimple coverage is not accomplished by the mere addition of very small dimples that do not effectively contribute to the creation of turbulence. In a preferred embodiment, the total number of dimples is about 300 to about 500 and at least about 80 percent of the dimples have a diameter of about 0.11 inches or greater, and, more preferably, at least about 90 percent of the dimples have a diameter of about 0.11 inches or greater. More preferably, at least about 95 percent of the dimples have a diameter of about 0.11 inches or greater.
In another embodiment of the present invention, the golf ball has an icosahedron dimple pattern. The pattern includes 20 triangles made from about 362 dimples and does not have a great circle that does not intersect any dimples. Each of the large triangles, preferably, has an odd number of dimples (7) along each side and the small triangles have an even number of dimples (4) along each side. To properly pack the dimples, the large triangle has nine more dimples than the small triangle. In another embodiment, the ball has five different sizes of dimples in total. The sides of the large triangle have four different sizes of dimples and the small triangles have two different sizes of dimples.
In yet another embodiment of the present invention, the golf ball has an icosahedron dimple pattern with a large triangle including three different dimples and the small triangles having only one diameter of dimple. In a preferred embodiment, there are 392 dimples and one great circle that does not intersect any dimples. In another embodiment, more than five alternative dimple diameters are used.
In one embodiment of the present invention, the golf ball has an octahedron dimple pattern. The pattern includes eight triangles made from about 440 dimples and has three great circles that do not intersect any dimples. In the octahedron pattern, the pattern includes a third set of dimples formed in a smallest triangle inside of and adjacent to the small triangle. To properly pack the dimples, the large triangle has nine more dimples than the small triangle and the small triangle has nine more dimples than the smallest triangle. In this embodiment, the ball has six different dimple diameters distributed over the surface of the ball. The large triangle has five different dimple diameters, the small triangle has three different dimple diameters and the smallest triangle has two different dimple diameters.
The present invention is also directed to defining the dimple profile on a golf ball by revolving a catenary curve about its symmetrical axis. In one embodiment, the catenary curve used to define a golf ball dimple is a hyperbolic cosine function in the form of:
Y=(d(cos h(ax)xe2x88x921))/(cos h(ar)xe2x88x921)
where:
Y is the vertical distance from the dimple apex,
x is the radial distance from the dimple apex,
a is the shape constant;
d is the depth of the dimple, and
r is the radius of the dimple (r=D/2)
D is the dimple diameter.
In one embodiment, at least 10 percent of the dimples have a shape defined by the revolution of a catenary curve. In another embodiment, at least 10 percent of the dimples have a shape factor, a, of greater than 60. In yet another embodiment, at least two different catenary shape factors are used to define dimple profiles on the golf ball. In one embodiment, at least 20 percent of the dimples have a catenary shape factor of less than 60 and at least 20 percent of the dimples have a shape factor of greater than 70. In another embodiment, at least three dimple profiles on the golf ball are defined by at least three different catenary shape factors.